Everything! Ok not absolutely everything but...
1. I dislike the 2 gold per turn per unit
2. I dislike the low unit support.
3. I dislike the WW.
4. I dislike the no MP.
5. I dislike having a small army.
6. I dislike the slow science rate because you have to increase the lux slider a lot due to WW.
Fair enough. I think Sashie VII has addressed all of these pretty well. Clearly, the increased support and absence of WW make Monarchy
the choice for AW games. But the extra unit support offered by Monarchy is only good if you're fielding the largest army that your gov't allows. In other words, you're wasting gold if you field anything smaller, because the gold that you're saving on unit support can't be used for anything else. Even though Republic offers less unit support, more gold is freed up for science or luxes.
Of all of the things that you've mentioned, they are all manageable in Republic. Nobody likes the 2gpt for over-the-limit unit support. But get enough towns down (which requires warring to clear out some room), and the commerce bonus overtakes the unit support problem. In my games, Republic stays hard on my economy until probably the middle of the MA. But after that, it really starts to take off. WW is a matter of fighting on your terms, not the AI's. Use the terrain and minimize losses. How high are you having to run your lux slider in Republic?
On the science issue, yes, you'll have to turn down the science slider for a little while after switching. But once you get your empire laid out and "tuned" for Republic, you'll easily outrun the AI. Besides, a little crafty trading goes a long way to overcoming that problem.
I've heard the same thing about a Republic at 50% doing the same research as Monarchy at 100%, but like Sashie VII, I haven't tested it. I don't have access to CA2 at the moment, but you can use the Economy tab in that program to test it.
Edit: Aceman101, if you really want to see Republic at its finest, try it out with a commercial civ. As you now have C3C, the Iroquois or the Romans come to mind. The Iros have, of course, the Mounted Warrior and start with, IIRC, Alphabet and Pottery. (IIRC, you're less than thrilled with the MW, but the IROs still start with Alphabet for the Rep. Slingshot & the ability to build granaries). The Romans start with Warrior Code and Alphabet, for early archers and a good jump on the Republic slingshot.